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Question
I need to find the limit as x-->+INF for the function f(x)=(sqrt(x^2+x)-x). I having trouble with it thanks!
We will use the trick : √a-√b=(a-b)/(√a+√b) .
This will gives us :
√(x²+x) - x = [x²+x-x²] / [√(x²+x) + x] = x/[√(x²+x) + x]=
1/[1+√(1+ 1/x)] . Therefore :
Lim 1/[1+√(1+ 1/x)] = 1/[1+√(1+ 1/∞)] = 1/[1+√(1+0)] = ½ .
x->∞
Alon.
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Alon Mandes
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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
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5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" ,
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M.A in Mathematics & Bs.c in Electronics.
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